How can I define a function that takes a list of reals?

Question

I'm trying to define a function f which takes a list of reals. My purpose is to build a function which I can give a list of reals, integers or strings and have it build an appropriate probability distribution for.

So I'd like to do something like

f[{samples_Real}]:=makeRealDist[samples];
f[{samples_Integer}]:=makeInteger[samples];
f[{samples_String}]:=makeCategoricalDist[samples];

I can easily match on Real/Integer/Strings. The part I can't figure out is how to match on a list of Real/Integer/String.

Answer 1

I feel that the basics of this topic are well covered in my answer to:

• Can a function be made to accept a variable amount of inputs?

Once you have read that and understand BlankSequence, Repeated, and Pattern you will understand that you could use either of these:

f1[samples : {__Real}]   := makeRealDist[samples]
f2[samples : {_Real ..}] := makeRealDist[samples]

If you wish to permit integers, fractions, etc, you can use NumberQ or perhaps even NumericQ.
Viable semantics include:

f3[samples_List] /; VectorQ[samples, NumberQ] := makeRealDist[samples]
f4[samples : {__?NumberQ}] := makeRealDist[samples]

Timings will show that the first forms (f1 and f3) are to be preferred:

SetAttributes[timeAvg, HoldFirst]
timeAvg[func_] := Do[If[# > 0.3, Return[#/5^i]] & @@ Timing@Do[func, {5^i}], {i, 0, 15}]

packed = Range[1, 1000, 0.0001];
timeAvg @ #[packed] & /@ {f1, f2, f3, f4}

{3.67616*10^-7, 0.1404, 5.59104*10^-7, 1.201}